caa a22 4500 469069066 CHVBK 20180323132916.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF02808056 doi (NATIONALLICENCE)springer-10.1007/BF02808056 The category of a map and the grade of a module [Elektronische Daten] [Y. Felix, S. Halperin, J. Thomas] Letf: Y → X be a continuous map between connectedCW complexes. The homologyH * (F) of the homotopy fibre is then a module over the loop space homologyH * (ΩX). Theorem:If H * (F; R) and H * (ΩX; R) are R-free (R a principal ideal domain) then for some H * (ΩX; R)-projective module P=P>0 and for some m ≤ cat f: $$Ext_{H_ * (\Omega X)}^m (H_ * (F);P) \ne 0.$$ Some applications are also given. Hebrew University, 1992 Felix Y. Institut de Mathématiques, Université Catholique de Louvain, B-1348, Louvain la Neuve, Belgium aut Halperin S. Physical Sciences Division, Scarborough College, University of Toronto, M1C 1A4, Scarborough, Canada aut Thomas J. U.F.R. de Mathématiques, Université de Lille Flanders, Artois, 59655, Villeneuve d'Ascq, France aut Israel Journal of Mathematics Springer-Verlag 78/2-3(1992-10-01), 177-196 0021-2172 78:2-3<177 1992 78 11856 https://doi.org/10.1007/BF02808056 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808056 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Felix Y. Institut de Mathématiques, Université Catholique de Louvain, B-1348, Louvain la Neuve, Belgium aut NATIONALLICENCE 700 1- Halperin S. Physical Sciences Division, Scarborough College, University of Toronto, M1C 1A4, Scarborough, Canada aut NATIONALLICENCE 700 1- Thomas J. U.F.R. de Mathématiques, Université de Lille Flanders, Artois, 59655, Villeneuve d'Ascq, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 78/2-3(1992-10-01), 177-196 0021-2172 78:2-3<177 1992 78 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer